If [x+6]+[x+3] ≤ 7 and let call its solution as set A and set B is the solution of inequality 35x-8 < 3-3x.
Let α,β, and γ be real numbers. Consider the following system of linear equations:
x + 2y + z = 7
x + αz = 11
2x - 3y + βz = γ
Match each entry in List I to the correct entries in List II
List I | List II | ||
(P) | If β=\(\frac{1}{2}\)(7α - 3) and \(\gamma\)=28, then the system has | (1) | a unique solution |
(Q) | If β=\(\frac{1}{2}\)(7α - 3) and \(\gamma\)\(\neq\)28, then the system has | (2) | no solution |
(R) | If β\(\neq\)\(\frac{1}{2}\)(7α - 3) where \(\alpha\)=1 and \(\gamma\)\(\neq\)28, then the system has | (3) | infinitely many solutions |
(S) | If β\(\neq\)\(\frac{1}{2}\)(7α - 3) where \(\alpha\)=1 and \(\gamma\)=28, then the system has | (4) | x = 11, y = - 2 and z = 0 as a solution |
(5) | x = -15 , y = 4 and z = 0 as a solution |
The expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’ are called linear inequalities. These values could be numerical or algebraic or a combination of both expressions. A system of linear inequalities in two variables involves at least two linear inequalities in the identical variables. After solving linear inequality we get an ordered pair. So generally, in a system, the solution to all inequalities and the graph of the linear inequality is the graph representing all solutions of the system.
Follow the below steps to solve all types of inequalities: